Problem: Given $ m \angle MON = 4x + 30$, $ m \angle LOM = 4x + 31$, and $ m \angle LON = 117$, find $m\angle MON$. $O$ $L$ $N$ $M$
From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {4x + 31} + {4x + 30} = {117}$ Combine like terms: $ 8x + 61 = 117$ Subtract $61$ from both sides: $ 8x = 56$ Divide both sides by $8$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 4({7}) + 30$ Simplify: $ {m\angle MON = 28 + 30}$ So ${m\angle MON = 58}$.